Three-Phase Inclusions of Arbitrary Shape With Internal Uniform Hydrostatic Stresses in Finite Elasticity
Bibliographic record
Abstract
We study the internal stress field of a three-phase two-dimensional inclusion of arbitrary shape bonded to an unbounded matrix through an intermediate interphase layer when the matrix is subjected to remote uniform in-plane stresses. The elastic materials occupying all three phases belong to a particular class of compressible hyperelastic harmonic materials. Our analysis indicates that the internal stress field can be uniform and hydrostatic for some nonelliptical shapes of the inclusion, and all of the possible shapes of the inclusion permitting internal uniform hydrostatic stresses are identified. Three conditions are derived that ensure an internal uniform hydrostatic stress state. Our rigorous analysis indicates that for the given material and geometrical parameters of the three-phase inclusion of a nonelliptical shape, at most, eight different sets of remote uniform Piola stresses can be found, leading to internal uniform hydrostatic stresses. Finally, the analytical results are illustrated through an example.
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How this classification was reachedexpand
Full frame distilled prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. Learned from the 10,348 direct Codex labels and 10,348 direct Gemma labels. Candidate is the union of thresholded teacher heads; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels or direct frontier model labels.
Codex and Gemma teacher scores by category
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.000 | 0.000 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.000 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.000 | 0.000 |
Machine scores (provisional)
The two teacher heads of the student model, read on this work. A score orders the frame for review; it never asserts a category, and the validation status ships verbatim with every row.
Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
score_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from itClassification
machine, unvalidatedMachine predicted; a candidate call from one teacher head, not a consensus.
How this classification was reached, model by model and score by score, is at the end of the page under "How this classification was reached".